Set 12, problem 2. Mickey saw 14 gnomes in the forest and 23 gnomes in the valley. How many gnomes did Mickey see?

Set 13.2. At first thirty-five fairies were flying about. Later twenty-seven more fairies began to fly about. In all, how many fairies were flying about?

Set 32.1. Just before high noon, Nancy saw seventy-eight elves playing in the valley. At high noon, there were only forty-two elves playing in the valley. How many elves had left the valley by high noon?

Set 32.2. According to the ancient Greeks, dryads were tree fairies. Penelope went one way and saw forty-six dryads. Perseus went the other way and saw some more dryads. Altogether they saw seventy-three dryads. How many dryads did Perseus see?

Set 41.3. When Linda looked the first time, she saw 211 elves frolicking in the glen. When she looked the second time, there were 272 elves frolicking in the glen. How many more elves did she see the second time?

Set 93.2. The shoemaker's wife made each of the 12 elves a pair of pants and 2 shirts. How many pieces of clothing did she make?

Set 102.12. The Fairy Queen flew 820 miles in 5 hours. How far did she fly in 1 hour?

Set 103.4. Four pounds of bananas cost the Fairy Queen one hundred fifty-six trinkets. Each pound of bananas cost how many trinkets?

Example 104.1. There were 30 leprechauns in the forest. Three fifths of them wore green jackets. How many leprechauns wore green jackets?

Example 104.2. Two thirds of the 24 elves worked in the toy factory. How many elves worked in the toy factory?

Practice problem 103.b. Two fifths of the 30 leprechauns guarded the treasure. How many leprechauns guarded the treasure?

Set 108.11. Thirteen little people came to the party every hour. After 11 hours, how many little people were at the party?

Set 114.4. Three eighths of the 32 elves packed toys on the sleigh. How many elves packed toys on the sleigh?

Practice problem 63.f. In old England 12 pence equaled 1 shilling. Merlin had 24 shillings. This was the same as how many pence?

Example 102.1. Forty percent of the leprechauns had never seen the pot of gold. If 480 leprechauns had seen the pot of gold, how many of the leprechauns had not seen it?

Example 102.2. Twenty-seven on the 45 elves who worked in the toy factory had to work the night shift. What percent of the elves had to work the night shift?

Set 105.18. Sixty percent of the gnomes were 3 feet tall or less. If there were 300 gnomes in all, how many were more than 3 feet tall?

Set 79.6. The survey found that only 2 out of 5 Lilliputians believe in giants. (1) According to the survey, what fraction of the Lilliputians do not believe in giants? (2) If 60 Lilliputians were selected for the survey, how many of them believe in giants? Lilliputians are mentioned again in set 118.10.

Set 14.1. The fairy queen found that 14 dryads could sit comfortably on one toadstool. If 780 dryads were coming to the forest convocation, how many toadstools would she have to provide so they could all sit comfortably?

Set 17.1. The third avatar of Happiness was a smile. Happiness is said to have 11 avatars in all. If she used 1 avatar a day, how many times would she appear as a smile in 10,802 days? Here Saxon is using the second dictionary definition of "avatar," meaning "an embodiment or concrete manifestation," not the definition from Hindu mythology meaning "the descent of a deity to the earth in an incarnate form," e.g., as a rabbit, a man, or some other living object.

Example 26.2. When Athena sprang in full armor from the head of Zeus, two other gods guessed the weight of her panoply. One guess was 41.082 kilograms and the other guess was 37.408 kilograms. What was the mean of the two guesses? This is a reference to Greek mythology. Zeus, king of the gods, had a bad headache. Vulcan, the metalworker god, kindly split his head open to relieve the pain. Out stepped Athena, the goddess of wisdom. Even the Greeks didn't believe this story by the time the New Testament was written.

Set 65.1. If 840 pixies had sad faces, how many pixies lived in the kingdom?

Set 78.2. The ratio of chimeras to gargoyles was 2 to 11. If there was a total of 380 chimeras, what was the total number of gargoyles?

Set 93.3. Hartzler multiplied his magic number by 14. Then he added 8. The result was 50. What was Hartzler's magic number?

Set 108.2. The ratio of ascetics to hedonists visiting the shrine was 4 to 7. If 4400 visited the shrine, how many were ascetics?

Set 110.1. Sixty percent of the populace were iconoclasts. If 16,000 were traditional, how many were iconoclasts?

Set 113.1. Twenty percent of the little people living in the forest suffered from agoraphobia, and they would not go into the clearing. If 1600 did not suffer from agoraphobia, how many little people lived in the forest?

Practice set 2.2. Seventy-eight percent of the dryads capered every time a star came out. If 110 did not caper, how many dryads were there?

Set 47.2. When Oberon and Titania assembled the little people, they found that the pixies and leprechauns were in a ratio to 3 to 13. If there were 6816 in all, how many were pixies? Oberon and Titania are the fairy king and queen in Shakespeare's "Midsummer Night's Dream."

Set 48.2. At the prestidigitator's banquet, the ratio of real magicians to charlatans was 7 to 2. If there were 324 at the banquet, how many were real magicians?

Set 66.3. After the temple was destroyed, Amenhotep found 1200 precious stones in the ruins. If 3 percent of these stones were rubies, how many rubies did Amenhotep find? Amenhotep was an Egyptian pharaoh.

Set 69.1. The troll became incensed when he saw the billy goats prancing across the bridge. Finally, he tore the bridge down--but not before 18 percent of the goats had crossed. If 45 goats had crossed, how many goats were there?

Set 83.3. The fairies outnumbered the hamadryads by 130 percent. If there were 460 fairies in the clearing, how many hamadryads were present?

Set 84.4. When the leprechauns ran into the forest, the number of little people present was decreased by 35 percent. If 105 ran into the forest, how many were left?

Set 99.5. When the stranger came into the forest, 37 percent of the little people ran to hide. If 2520 refused to hide, how many little people lived in the forest?

Set 103.5. Twenty-three percent of the newcomers thought there was no difference between a thaumaturge and a prestidigitator. If 3465 people believed that there was a difference, how many newcomers were there in all?

Set 9.1. The wood nymphs and the maids gamboled and frolicked before the banquet began. If 60 percent of those present were wood nymphs, and 160 maids were present, how many wood nymphs came to the banquet?

Set 11.1. Thirteen percent of the people believed in lycanthropes. If 5220 did not believe in lycanthropes, how many believed?

Set 44.1. A secret number was unearthed in the Mayan ruins. When the number was increased by 5 and this sum multiplied by -2, the result was 18 greater than six times the opposite of the number. What was the secret number found in the ruins?

Set 46.4. The ratio of fairies to elves was 7 to 2, and the number of fairies was 11 greater than 3 times the number of elves. How many of each were there?

Set 52.5. Queen Hatshepsut rode a litter at 2 kilometers per hour for the first part of the journey to the necropolis. She was going to be late, so she changed to a chariot traveling 8 kilometers per hour for the last part of the trip. If it was 28 kilometers to the necropolis and the trip took 8 hours, how far did she ride in the litter and how far did she ride in the chariot?

Set 25.1. On the 36-mile trip to the magic fountain, Alice walked at a brisk pace. On the way back, Alice doubled her pace. If the total trip took 6 hours, how fast did Alice travel on her trip to the magic fountain and on the return trip from the magic fountain?

Set 86.4. The level of the milk in the magic pitcher increased exponentially. When Griselda first looked, the level was 0.04 centimeters. Twenty seconds later the level was 2.6 centimeters. How long would it take for the level to increase to 16 centimeters?

Set EL1.4. Fiddlesticks sell for $100 each, but gnomes get a 10 percent discount. If a gnome purchased fiddlesticks in coins instead of dollar bills, the gnome gets 10 percent off of the discount price. what would a gnome who pays in coins have to pay for 5 fiddlesticks?

II. Good Problems

You may have noticed that over 4,000 problems in each Saxon math text are not questionable. In fact, many of them are highly meritorious. Almost alone among math textbook writers, Saxon includes problems that mention family members helping each other and children behaving virtuously. He also includes many problems that introduce children to the facts of history, science, and literature, and many more that are just plain fun. We have included some typical examples below.

Math 54

Set 15.1 Seventy-seven students ran in circles and waved their arms. Nineteen students watched in amazement. How many students were there in all?

Math 76

Set 106.3. If all the king's horses total 600, and all the king's men total 800, then what is the ratio of men to horses?

Math 65

Set 22.3. Grandpa has 10 quarters. If he gives each of his 3 grandchildren 3 quarters, how many quarters will he have left?

Set 76.6. William found $30,000 of misplaced money. The grateful owner gave William one tenth of the money as a reward. How much money did William get?

Math 76

Set 7.1. To earn money for gifts Debbie sold decorated pine cones. If she sold 100 cones at $0.25 each, how much money did she earn?

Set 71.3. The temperature on the moon ranges from a high of 134 degrees C to a low of about -170 degrees C. This is a difference of how many degrees?

Math 87

Set 16.1. Great Grandpa celebrated his seventy-fifth birthday in 1989. In what year was he born?

Set 30.3. The Byzantine Empire lasted from 395 to 1453. How many years did the Byzantine Empire last?

Set 83.1. With the baby in his arms Papa weighed 180 pounds. Without the baby in his arms Papa weighed 165 1/2 pounds. How much did the baby weigh?

Set 99.1. Use a ratio box to solve this problem. If 4 cartons are needed to feed 30 hungry children, how many cartons are needed to feed 75 hungry children?

Algebra 1/2

Set 77.1. A harsh law is called a draconian law after the Greek law-giver Draco. Two-fifths of the laws were draconian. If 42 laws were draconian, how many laws were there in all?

Set 114..2. The number that eschewed unauthorized assistance rose 260 percent in 1 month. If the number was 400 last month, what was the number this month?

Algebra 2

Set 40.1. Many students took a foreign language to increase their vocabularies and improve their grammar. These students earned 64 percent more than the others. How much did they make if the others earned $1,200,000?

Set 45.1. Since knowledge of chemistry is useful even in nonscientific fields of study, a majority of the students elected to take chemistry. If 38 percent did not take chemistry, how many students were there in all?

Set 84.1. The number who were admired varied inversely with the number who had a proclivity for bragging. When 80 bragged, only 20 were admired. How many were admired when 10 bragged?

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